If there's a God, or any kind of justice under the sky,
If there's a point, if there's a reason to live or die,
If there's an answer to the questions we feel bound to ask,
Show yourself! Destroy our fears! Release your mask!
Oh, yes, we'll keep on trying . . .
-- Queen, Innuendo (Despite the title, that song contains little or no sexual content, and, indeed, no content more offensive than the above.)
I understand why theists use the "if that was true life wouldn't be worth living" argument. Sure, it doesn't actually have any effect on the facts of the case. Maybe life just isn't worth living. But I know full well that if I thought believing something would make me want to kill myself, I would hesitate on the objectivity a little. More, I've got a moral sense as strong and passionate as any and if I thought believing something would make me do something seriously morally wrong, well, I might allow myself a little self-deception. Of course, you'd be a fool to expect something you believe because you can't live without believing it to be a reliable indicator of the sorts of conclusions you'd come to based on actual evidence. No doubt that's where the 'non-overlapping magisteria' rule comes from. It makes sense, when you think about it. Go ahead and believe in God if you need to, says that rule, but don't come whining when the fossil evidence contradicts the petty details of the structure you've taken on in an attempt to find purpose. There's no reason to expect agreement.
In atheist attempts to avoid making statements about the world which are not supported by evidence, I suspect some believers occasionally hear us as saying "Question everything, and discard anything that doesn't correspond to an objective phenomenon of the world outside our minds". That's not what we're saying. Indeed, that would be nihilism. Love is not an objective phenomenon of the world outside our minds, and nor is happiness.
At other times, while they understand atheism might not ask us to stop caring per se, believers might be afraid that they would stop caring if they didn't have the justification.
Does it scare you to consider the possibility that the care you feel is only in your mind, not justified by any certain logic of the world outside you? Then take yourself to the brink. Go there because it is a rite of passage, go there by reciting truths. The universe doesn't care if you live or die. You could kill yourself now, and the effect on the world in two hundred years might be large, but only by chaos theory, not by any effect that a historian could trace. You don't have to care. It would be just as logical not to. Say it and feel it and go to the brink and watch the nothingness bubble. It burns a little; maybe a lot; maybe it takes genuine care for the truth to force you to risk it. And it bubbles. You can't help it bubbling. Little bits of reality or imagination will insist on popping up, no matter how hard you try. So no-one will care in two hundred years. But people care now, don't they? It's a reflex, I think, you find yourself resurfacing for the sake of survival. Squash it. I dare you. But you're only allowed to use true statements. How about "But they don't have to care"? How about "But there's no reason to care if they care"? I bet you still do care. Can you make yourself stop? I can't. On this count, and on several others, the bubble just won't pop. The truth is not enough to sever you from your ability to care. It never could be.
You can go to the brink, but you take your humanity with you.
Now, here's the big question. Do you have to stop? Does caring about anything mean that you've abandoned the principles of truth that atheists claim to value? Are you believing anything false by caring? Well, if you ask me, the process of caring is not logically connected to the process of believing at all. Sure, there's a connection between what you believe and what you care about. If you believe your sister cares about you, for example, you might be more likely to care about her. But that's not a logical connection. It might perhaps be "little-'o' objective"; that's about the best you can do. There's really no logical connection either way. You don't logically have to care. You don't logically have to not care.
The rule isn't "Discard anything that can't be shown to correspond to an objective phenomenon of the world outside our minds". In my opinion, the rule is actually "Don't call anything an objective phenomenon without some evidence that it actually is one". That doesn't mean you're not allowed to care about the subjective or, indeed, to care subjectively.
You can't leave your subjectivity behind. And you don't have to. Aren't you glad?
Continued, because I've thought again and I don't like this post as it is:
I'm aware that there's another issue here. Can you be satisfied with the truths you have? Is it enough to know that you're here now, even if you don't have eternity? Is it enough for you that there are people you love and who love you -- is it enough to know that you may have to work to keep the real things in your life because you won't necessarily have God -- is it enough for you to care, well, just because you do?
I think, for most people, it is enough. I think there are far more people who think they can't do this than people who really can't. They haven't ever had to build a life based on things that a skeptical atheist can accept, and they just don't know how much there is to work with. But I've seen the nothingness and felt it burn and if running from it makes you run from atheism, well, I'm not going to shout at you and call you stupid. I'd rather just offer my hand.
 I borrow this terminology from Steve Novella here; thanks are due to Ordinary Girl in the comments of this post here on Elliptica for pointing me towards it. By "little-'o' objective" I mean based not on some objective fact of the world outside our minds but rather on some aspect that is near-universal within our minds.